Download Midterm Question - Western Engineering

The University of Western Ontario
Faculty of Engineering
Department of Mechanical & Materials Engineering
MME 2213 Engineering Dynamics
Mid-term Examination, Thursday 12 February 2009
Limited Open Book
2 hours Total for working
Intramural
AIDS: 8 1/2" x 11" Equation Aid Sheet allowed
Calculator (all calculators allowed)
Answer ALL questions
Questions are NOT of EQUAL value
Questions carry the number of marks indicated
Question 1 part marks are indicated
Total Marks 100
Cheating:
University policy states that cheating is a scholastic offense. The commission of a
scholastic offence is attended by academic penalties which might include expulsion
from the program. If you are caught cheating, there will be no second warning.
QUESTION 1
(Total marks 20)
Provide Brief Answers to the following:
(a) How would you find distance from a typical velocity-time (v-t) plot? Draw a v-t plot
illustrating a steadily increasing acceleration
[2 marks]
(b) State fundamental forms of Newton’s Law relating to translational and rotational motion
(Hint: I am not looking for F=ma)
[3 marks]
(c) Describe four possible orbits associated with central force motion and the corresponding
eccentricity (  ) values
[3 marks]
(d) Explain why the conservation of angular momentum holds in the case of central force
motion? Illustrate via a simple sketch
[3 marks]
Page 1 of 3
(e) State work energy principle and explain its relationship to the principle of conservation of
energy. State the fundamental assumption associated with application of this principle.
[3 marks]
(f) Define “coefficient of restitution” and explain its relevance to perfectly plastic impact.
[3 marks]
(g) A particle of mass m is considered to travel along a curvilinear path in two dimensions.
Using polar ( r   ) co-ordinate system, mark the relevant acceleration components and
their directions together with their names.
[3 marks]
QUESTION 2
(Total marks 25)
The polar coordinates of tip A of the crane shown in Figure 1 are given as functions of time by
r  12  0.4t 2 m and   0.02t 3 rad. Determine the velocity and acceleration of tip A in terms of
polar co-ordinates at t  2 seconds.
Figure 1 (For Question 2)
QUESTION 3
(Total marks 25)
Two blocks A and B connected via two frictionless pulleys and a cable as shown in Figure 3 are
pulled with an external force of 250 N. (a) Determine the relationship between the accelerations of
A and B assuming that the cable is inextensible (b) Determine the accelerations of blocks A and B
and the tension in the cable due to application of the external force neglecting all friction and
masses of the pulleys.
Figure 2 (for Question 3)
Page 2 of 3
QUESTION 4
(Total marks 30)
A satellite describes a circular orbit at an altitude of 19,019.4 km above the surface of the earth.
Determine (a) the decrease in speed required at point A for the satellite to enter an elliptic orbit of
minimum altitude 6345 km (b) the eccentricity  of the resulting elliptic orbit.
Figure 4 (for Question 3)
Page 3 of 3